Invitation to number theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Washington
Mathematical Association of America
[2017]
|
| Edition: | Second edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | x, 134 Seiten Illustrationen |
| ISBN: | 9780883856536 |
Staff View
MARC
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| 245 | 1 | 0 | |a Invitation to number theory |c Oystein Ore ; revised and updated by John J. Watkins and Robin Wilson |
| 250 | |a Second edition | ||
| 264 | 1 | |a Washington |b Mathematical Association of America |c [2017] | |
| 264 | 4 | |c © 2017 | |
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Record in the Search Index
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| adam_text | Contents
Preface to the Revised Edition vii
1 Introduction 1
1.1 History ................................................... 1
1.2 Numerology............................................... 1
1.3 The Pythagorean Problem ................................... 2
1.4 Figurate Numbers........................................... 4
1.5 Magic Squares ............................................. 7
2 Primes 15
2.1 Primes and Composite Numbers.............................. 15
2.2 The Sieve of Eratosthenes ................................ 17
2.3 Mersenne Primes......................................... 19
2.4 Fermat Primes............................................. 22
3 Divisors of Numbers 25
3.1 The Fundamental Factorization Theorem..................... 25
3.2 Divisors.................................................. 27
3.3 Problems Concerning Divisors.............................. 29
3.4 Perfect Numbers .......................................... 31
3.5 Amicable Numbers.......................................... 33
4 Divisors and Multiples 35
4.1 Greatest Common Divisor................................... 35
4.2 Relatively Prime Numbers.................................. 37
4.3 Euclid’s Algorithm........................................ 38
4.4 Least Common Multiple..................................... 41
5 The Pythagorean Theorem 43
5.1 Preliminaries............................................. 43
5.2 Solving the Pythagorean Equation.......................... 44
5.3 Pythagorean Triangles .................................... 47
5.4 Related Problems........................................ 50
5.5 Fermat’s Last Theorem..................................... 53
IX
x Contents
6 Number Systems 57
6.1 Numbers for the Millions.............................. 57
6.2 Other Systems.......................................... 58
6.3 Comparing Number Systems............................... 61
6.4 Early Calculating Devices ............................. 64
6.5 Computers and their Number Systems..................... 66
6.6 Cryptarithms........................................... 68
7 Congruences 73
7.1 What is a Congruence?.................................. 73
7.2 Properties of Congruences.............................. 74
7.3 The Algebra of Congruences............................. 76
7.4 Powers of Congruences.................................. 78
7.5 Fermat’s Little Theorem ............................... 80
7.6 Euler’s Phi Function .................................. 83
8 Applying Congruences 87
8.1 Checking Computations ................................. 87
8.2 The Days of the Week ................................. 91
8.3 Tournament Schedules................................... 95
8.4 Prime or Composite?.................................... 97
9 Cryptography 101
9.1 Secret Codes ..........................................101
9.2 Caesar Ciphers ........................................102
9.3 Vigenere Ciphers.......................................105
9.4 Public Key Ciphers.....................................108
10 Solutions to Selected Problems 115
References 129
Index 131
|
| any_adam_object | 1 |
| author | Ore, Øystein 1899-1968 |
| author_GND | (DE-588)117717444 (DE-588)135619629 (DE-588)141760176 |
| author_facet | Ore, Øystein 1899-1968 |
| author_role | aut |
| author_sort | Ore, Øystein 1899-1968 |
| author_variant | ø o øo |
| building | Verbundindex |
| bvnumber | BV044745176 |
| classification_rvk | SK 180 |
| ctrlnum | (OCoLC)1031440119 (DE-599)BVBBV044745176 |
| discipline | Mathematik |
| edition | Second edition |
| format | Book |
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| id | DE-604.BV044745176 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:01:02Z |
| institution | BVB |
| isbn | 9780883856536 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030140960 |
| oclc_num | 1031440119 |
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| physical | x, 134 Seiten Illustrationen |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | Mathematical Association of America |
| record_format | marc |
| spelling | Ore, Øystein 1899-1968 Verfasser (DE-588)117717444 aut Invitation to number theory Oystein Ore ; revised and updated by John J. Watkins and Robin Wilson Second edition Washington Mathematical Association of America [2017] © 2017 x, 134 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s DE-604 Watkins, John J. 1946- (DE-588)135619629 oth Wilson, Robin J. 1943- (DE-588)141760176 oth Erscheint auch als Online-Ausgabe 10.1007/978-0-88385-992-6 Erscheint auch als Online-Ausgabe 978-0-88385-992-6 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030140960&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ore, Øystein 1899-1968 Invitation to number theory Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4067277-3 |
| title | Invitation to number theory |
| title_auth | Invitation to number theory |
| title_exact_search | Invitation to number theory |
| title_full | Invitation to number theory Oystein Ore ; revised and updated by John J. Watkins and Robin Wilson |
| title_fullStr | Invitation to number theory Oystein Ore ; revised and updated by John J. Watkins and Robin Wilson |
| title_full_unstemmed | Invitation to number theory Oystein Ore ; revised and updated by John J. Watkins and Robin Wilson |
| title_short | Invitation to number theory |
| title_sort | invitation to number theory |
| topic | Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Zahlentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030140960&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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